Why doesn’t the United States need to train lots of mathematicians? Why don’t Americans memorize a lot of mathematics in school?
Why do Asian kids outperform Western kids in math? | by Malcolm Gladwell at https://www.youtube.com/watch?v=8Wo31YeAI0Q
Why don’t Americans memorize a lot of mathematics in school? by Richard Collins
Mostly kids in the United States are not expected to do anything. About one in a thousand who do put in effort is enough to solve the few problems that come up. “Why memorize things you will never use ?” is the most common thing to hear. It is also common that good teachers who do care and are skills are extremely rare. No American kids are challenged in school unless they happen to hit one of those rare teachers. The test score matter only when school use tests any more. I always did very well, but when I first got to college my room mate had made perfect score in every test he took. So skill is not the reason, he wanted to go in a particular direction so he did what was necessary. Most students in the United State there are few jobs that actually use mathematics. If people like moving symbols around, they buy a symbolic math tool and use that. Or today they hack together and AI and get the AI to do the math, the programming, the things they want to do. Memorizing equations, math rules and stuff is completely useless. Using math is rarely a complete answer any where. I know most all of mathematics because I have to review all content on the Internet. There is a lot of math talked about, but it is rarely used for anything practical. Engineers and scientists is is converted (manually and badly) into computer code and models and apps and software.
Taking tests is useless. Nowadays and for much of the last 50+ years I have been working in large organizations, you just hire the Asian kids (respectfully) or the Indian kids or ones form many dozens of countries in the world.
Eventually the AIs will do it all. If anyone has asked me we would already have it. I am trying to implement “all mathematics for all humans using the Internet with AIs at global scale with all math knowledge” It is possible and not that hard now. So forcing billions of people (about 2 billion kids from 4-24 who are learning for the first time) to memorize that? Kind of a waste. If the computer does all the steps there are lots of problems I would use that if it fits. But much of the data in the world does NOT fit analytic curves, complicated but too simplistic boundary conditions, Like I say, I know pretty much every quantitative and analytic discipline and that old blackboard math is mostly a waste of time, unless you like playing those kinds of games. Go and check if you feel you are supposed to do that an see if some enthusiastic adult is responsible for pushing you that way.
The whole economy of the United States will barely support 1 in a hundred going into math and science. Anything else generate tens of millions of over educated and underemployed humans. I feel sorry for couple of countries that have more than a billion people each, where they are using 50 or 100 year old market data and encouraging EVERY kid to memorize math equations, to practice endless symbols manipulations on paper. It has slight value for impressing younger kids, zero value in attracting a mate, and little value in getting jobs unless you want to be promoting something you learned.
I have a pretty good sense of where the humans species could go. Elon Musk talks about solar system exploration and development. But he is not rich enough to do it alone and as his clients get used to him, they will drag it out and erode his enthusiasm probably.
In the countries that do teach mathematics of that old type, are those people doing well? Most of them try to get to the United States because mathematics skills are highly valued, in limited amounts. The US values engineers more than mathematicians and theoretical or pure math, almost not at all. Because those old problems that were solved long ago and form the basis of what gets regurgitated on blackboard and video screen and paper books – is mostly not that useful. And it if is useful it has been converted to software and you can buy it if you can afford it.
I often read dozens up to hundreds of papers each week. And most are filled with math. But I mostly never have to use more than fairly simple stuff that only requires a solid understanding of linear algebra, calculus, differential equations, and an ability to use computers. Could I do a lot more? It is fun, but mostly useless. If you go deep, there is no one to talk to. And like I said jobs are few and far between because those old goals are not the ones that are valued now.
I feel really sorry for India and China. The kids from there (my differential equation teacher in high school in 1966 was from India). But he only taught from the book. There are a lot of over educated and underemployed.. And they have not clue how to use the Internet, how to work together, how to prevent discrimination, how to make sure everyone is treated fairly, well fed and cared for, reaches their full potential.
I would say that one of my favorite books in my lifetime is Radiative Transfer by Chandrasehkar. But his mathematical notation is atrocious if you want to process and model real data. It is a paper method, not a computer method. My first day at Case Institute of Technology 1967 I got a job with the Mathematics Department teaching kids in numerical calculus how to use the computer. I could see what they had to do in Mathematics and it was pretty dreadful. The ones who went to computing, physics, engineering did OK, but a couple of decades later all those people were out of work or working at half or third salaries. One of my best friend during college was an accountant. The ones in finance, the ones that went into brokerage did well. But most of them did not use mathematics, it was hard work, attention to detail, awareness of the needs of others and a strong dose of passion that seemed to make a difference.
I did work much of my life as a Mathematical Statistician but those jobs are pretty scarce. Much of my time was definitely not mathematical, more statistical, lots of computing, managing people, motivating people. It is rather difficult to convince people. A good salesperson who can manipulate emotions is way better than a reasoned argument. I did work with all the data on countries, financial models, industry projections, optimizing processes, constrained optimizations. Those were good and useful skills, but never anyone to talk to. People would accept my help, usually accept my recommendations, fund the projects. But talk about mathematics or use it, not really. My first fulltime job was tracking all the objects in orbit (1970) and that did use a kind of half mathematics and half computing language. It was explained to me as forward and inverse problems, but all my life I simply called it “constrained optimization” or “modeling” or “budgeting” or “projections”. That is useful but it is a lonely job.
When I worked for Phillips Petroleum in their Business Office, the groups was called “Business Intelligence” One thing I did one time. I took the model for the upstream (exploration, development, pipelines, storage and some processing ) then the model for the refinery and chemicals, and the marketing and distribution and put them all together. They were all in separate spreadsheets mostly so I combined them, added my own optimization and solver (and ran sensitivity analysis) on the combined model. Combining the assumptions embedded in the separate models gave me much more robust and consistent and easier to maintain real work data. But that was not mathematics, it was not really computing, it was not accounting, it was not model making. but rather “look at a problem, all the data, and all the computing, and make it work better. Maybe that is pretty common now, it is how I did things and there was no one to ask or help.
When i was working with census data for the first time, I was a “statistician” surveying whole cities in Texas to determine health status, but the data was used to set up systems to keep track of health and situation of every individual so that nurses could help them keep healthy.We put the data on maps (paper tracing ) and used the data to tell what resources were needed. My boss came to me one day and asked me if I could help justify two new regional offices (Texas has 254 counties, and 11 health regions). He explained that the they had asked for bids, but they were coming in more than a million dollars and up to two years. He and his boss did not want to wait that long. So I said if he could get me a few clerks, I could probably do it in a couple of months. So 4 very young girls with not a lot of mathematics, but skill with numbers. I got some programmable calculators and we uses that to project the population of each country by age and sex out 10 years and estimated the requirements of health. We compiled all the data from the census and every other source with chapters for each county (about 25>) and regional summary. That first region took a month. Then those young ladies did the other one by themselves. Much can be done with humans, humans can do a LOT on their own without computers (This was early 1970s) and personal computers were more than a decade in the future.
I did solve one mathematics problem that was fun. If you have a table with rows and columns, integer entries and only row and column sums how many possible tables are there where any cell is specified. It took me a week of evenings to work out all of them, And I found it is very easy to calculate. But only many years later I was reading Abramowitz and Stegun Handbook of Mathematical Functions and recognized the numbers, So it is nothing really new. I spent a could of years on Fermats problem and got nice practice with raising infinite and finite series to integer powers. It was the same as the Catalan problem but no one cares about things like that.
So overall I think if you like it do it,. Your are not going to be thanked. You will never make a lot of money. You will never have decent tools. You wil get some nice hard problems now and then, but no one will care or notice.
When I was going to University of Maryland College Park studying gravitation, astrophysics, partial differential equation, aerodynamics I got a job working with Steve Klosko at Wolfe Research on a NASA contract where we too observed satellite orbits, radar and laser tracking data, altimeter data and solved for the earth gravitational potential field, It has been a long time now but they were GEM models and something like 32×32.now they are 2160×2160. The data from my earlier job at the CIA with orbits had NavSpasur data which was one observation per orbit, That was nice to use analytics solutions to get initial values but ticklish to get it close enouhgh to converge with the full model. I learned the value of double precision and putting enough effort into good estimate models to get you close enough so it was not necessary Steve came to me one day with some data and said someone needs a Kalman filter so they could take the C-band real time data and give control signals to a laser to track the satellites. It only took an hour or so, but it always struck me as an interesting problem. When I looked up what a Kalman filter was, it was easy, The “Star Wars Strategic Defense Initiative was not until 1983 and this was 1978. But it struck me that the skills were around for that sort of thing pretty much all the time.
This relates to “Why don’t American memorize a lot of mathematics in school?” It is mostly that only 1 in a hundred are needed. There are not that many jobs for full time mathematicians, most of the problems were solved long ago and you just look them up, or buy some software or search the web or ask your AI, or hire someone from another country. When I was in my third year of college at UWF I had a job grading papers for the advanced aerospace engineering mathematics class, That was maybe a graduate course, but it was basic algebra and elementary powers of infinite series, Finding recursions. Fun, tedious, but not hard. Most of the United States there is mathematics embedded all over the place, If you pick up a neutron star model or a stellar nucleo-synthesis model, it is all simple math that you learn in high school. The computer part is usually badly documented but it is more tedious than difficult.
Looking back over 60 years, most of that working. I did use mathematics a fair amount and it did contribute to solving work related problems. And a lot of problems not work related but that needed to be solved.
This was useful to me, because I often think about friends who come from other countries. They have different education systems and different priorities.
Why don’t Americans memorize a lot of mathematics in school? Well they actually do, but mostly do not talk about it. And it is such a part of American society, you just grab people and do the job when it comes up.
Richard Collins, The Internet Foundation
